where \(\mathrm {Var}_{\hat{\mathbb {P}}_T}(\ell (x, \xi ))\)  denotes the empirical variance of the loss. Although the term SVP was coined by [1]} in the context of machine learning, the benefits of variance regularization were documented much earlier by [2]} in the context of portfolio selection. This regularized formulation is biased towards decisions for which the empirical variance of the cost is low rather than high. In particular, [1]} show that SVP enjoys out-of-sample performance guarantees of the form
\(\mathbb {P}^{\infty }\left(\mathbb {E}_{\mathbb {P}}(\ell (x, \xi ))>\mathbb {E}_{\hat{\mathbb {P}}_T}(\ell (x, \xi )) + \sqrt{\frac{2a}{T}} \sqrt{\mathrm {Var}_{\hat{\mathbb {P}}_T}(\ell (x, \xi ))}+ C\frac{a}{T}\right)\le 2e^{-a},\) 
